Figure shows variation of Coulomb force (F) acting between two point charges with \( \frac{1}{r^2} \), \( r \) being the separation between the two charges \( (q_1, q_2) \) and \( (q_2, q_3) \). If \( q_2 \) is positive and least in magnitude, then the magnitudes of \( q_1, q_2 \), and \( q_3 \) are such that:
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Remember that the Coulomb force is proportional to the product of the charges and inversely proportional to the square of the distance between them. If one charge is smaller, it produces less force.
The question relates to the variation of the Coulomb force \( F \) with respect to \( \frac{1}{r^2} \) between two point charges. We need to determine the relationship between the magnitudes of \( q_1 \), \( q_2 \), and \( q_3 \) given \( q_2 \) is positive and the smallest in magnitude.
The Coulomb's law states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) is given by:
\( F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \)
where \( k \) is Coulomb's constant.
Given that the graph indicates how force \( F \) varies with \( \frac{1}{r^2} \), the slope of this relationship will depend on the product of the charges \( |q_1 \cdot q_2| \). The magnitude of \( F \) is directly proportional to the product of the magnitudes of the charges.
From the information provided, \( q_2 \) has the least magnitude and is positive. The relationship between the magnitudes of \( q_1 \), \( q_2 \), and \( q_3 \) must account for this, leading us to: \( q_2<q_1<q_3 \)
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Approach Solution -2
To solve the problem, we need to understand the behavior of the Coulomb force between point charges as described by Coulomb's Law:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \( F \) is the force between the charges, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the point charges, and \( r \) is the distance between them.
The problem states that \( q_2 \) is positive and is the least in magnitude. We need to determine the relationship between \( q_1 \), \( q_2 \), and \( q_3 \).
Given the force variation with \( \frac{1}{r^2} \), it implies a linear relationship if plotted with the variables appropriately transformed, ensuring that the product of the charges influences the slope. Since \( q_2 \) is the least and positive, any comparison would show that:
Given \( q_2 \lt q_1 \lt q_3 \), the influence of \( q_2 \) being the smallest would be appropriate as the force diminishes more quickly with less product magnitude when compared with \( q_1 \) and \( q_3 \).
